{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UPGI5D5KU4NCMOUI6COLGPSLX4","short_pith_number":"pith:UPGI5D5K","canonical_record":{"source":{"id":"1809.10015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2018-09-26T14:22:07Z","cross_cats_sorted":[],"title_canon_sha256":"954c0f0f34214f5296458ee18ec537ab8b173a54c02837f7ee3f0685695674df","abstract_canon_sha256":"e33c75185ee277e4cc816647d2aeb87d26a34dcfe49a1df2080a6eef30153735"},"schema_version":"1.0"},"canonical_sha256":"a3cc8e8faaa71a263a88f09cb33e4bbf1cf62defe03c235ec5c277299de94af3","source":{"kind":"arxiv","id":"1809.10015","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10015","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10015v1","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10015","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"UPGI5D5KU4NC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UPGI5D5KU4NCMOUI","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UPGI5D5K","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UPGI5D5KU4NCMOUI6COLGPSLX4","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2018-09-26T14:22:07Z","cross_cats_sorted":[],"title_canon_sha256":"954c0f0f34214f5296458ee18ec537ab8b173a54c02837f7ee3f0685695674df","abstract_canon_sha256":"e33c75185ee277e4cc816647d2aeb87d26a34dcfe49a1df2080a6eef30153735"},"schema_version":"1.0"},"canonical_sha256":"a3cc8e8faaa71a263a88f09cb33e4bbf1cf62defe03c235ec5c277299de94af3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:42.896868Z","signature_b64":"+FdpP9pJv5n3QTZavb1BAacY7SFv7135FRonYCl5a+ATnGqplWOqKvKfgeZG+xHiXOpPpGB9bUUWFzjVdX/jAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3cc8e8faaa71a263a88f09cb33e4bbf1cf62defe03c235ec5c277299de94af3","last_reissued_at":"2026-05-18T00:04:42.896190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:42.896190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10015","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJGzISb5A1G/mYzqALgxEaFk3X4nzQI3WyhL7dx5QikRM1blLJVjY0z5JUBJYIS8S9oLciySSi2o0XwQtLd/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:14:52.899082Z"},"content_sha256":"98d95bce5aa724b08849d7ad648dfde7be1078eff3cfa2aea9bf6f16ec9d77a1","schema_version":"1.0","event_id":"sha256:98d95bce5aa724b08849d7ad648dfde7be1078eff3cfa2aea9bf6f16ec9d77a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UPGI5D5KU4NCMOUI6COLGPSLX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Risk sharing for capital requirements with multidimensional security markets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.RM","authors_text":"Felix-Benedikt Liebrich, Gregor Svindland","submitted_at":"2018-09-26T14:22:07Z","abstract_excerpt":"We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and have access to different security markets. We discuss conditions under which there exists a representative agent. Thereafter, we study two frameworks of capital adequacy more closely, polyhedral constraints and distribution based constraints. We prove existence of optimal risk allocations and equilibria within these frameworks and elaborate on their robustness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10015","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"be8xewrIbsqMYg1GDPQKtLKsRmpg/vdZwnCIouxOQ5hZElov6cCTUdEjwUJr55cJklC/DlSD79WKNpIEh1yTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:14:52.899779Z"},"content_sha256":"1008a825d85f4ed93db62200f1fb8f395d852eb54f179f8bec315cef5e377b68","schema_version":"1.0","event_id":"sha256:1008a825d85f4ed93db62200f1fb8f395d852eb54f179f8bec315cef5e377b68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPGI5D5KU4NCMOUI6COLGPSLX4/bundle.json","state_url":"https://pith.science/pith/UPGI5D5KU4NCMOUI6COLGPSLX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPGI5D5KU4NCMOUI6COLGPSLX4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T23:14:52Z","links":{"resolver":"https://pith.science/pith/UPGI5D5KU4NCMOUI6COLGPSLX4","bundle":"https://pith.science/pith/UPGI5D5KU4NCMOUI6COLGPSLX4/bundle.json","state":"https://pith.science/pith/UPGI5D5KU4NCMOUI6COLGPSLX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPGI5D5KU4NCMOUI6COLGPSLX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UPGI5D5KU4NCMOUI6COLGPSLX4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e33c75185ee277e4cc816647d2aeb87d26a34dcfe49a1df2080a6eef30153735","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2018-09-26T14:22:07Z","title_canon_sha256":"954c0f0f34214f5296458ee18ec537ab8b173a54c02837f7ee3f0685695674df"},"schema_version":"1.0","source":{"id":"1809.10015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10015","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10015v1","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10015","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"UPGI5D5KU4NC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UPGI5D5KU4NCMOUI","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UPGI5D5K","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:1008a825d85f4ed93db62200f1fb8f395d852eb54f179f8bec315cef5e377b68","target":"graph","created_at":"2026-05-18T00:04:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and have access to different security markets. We discuss conditions under which there exists a representative agent. Thereafter, we study two frameworks of capital adequacy more closely, polyhedral constraints and distribution based constraints. We prove existence of optimal risk allocations and equilibria within these frameworks and elaborate on their robustness","authors_text":"Felix-Benedikt Liebrich, Gregor Svindland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2018-09-26T14:22:07Z","title":"Risk sharing for capital requirements with multidimensional security markets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10015","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:98d95bce5aa724b08849d7ad648dfde7be1078eff3cfa2aea9bf6f16ec9d77a1","target":"record","created_at":"2026-05-18T00:04:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e33c75185ee277e4cc816647d2aeb87d26a34dcfe49a1df2080a6eef30153735","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2018-09-26T14:22:07Z","title_canon_sha256":"954c0f0f34214f5296458ee18ec537ab8b173a54c02837f7ee3f0685695674df"},"schema_version":"1.0","source":{"id":"1809.10015","kind":"arxiv","version":1}},"canonical_sha256":"a3cc8e8faaa71a263a88f09cb33e4bbf1cf62defe03c235ec5c277299de94af3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3cc8e8faaa71a263a88f09cb33e4bbf1cf62defe03c235ec5c277299de94af3","first_computed_at":"2026-05-18T00:04:42.896190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:42.896190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+FdpP9pJv5n3QTZavb1BAacY7SFv7135FRonYCl5a+ATnGqplWOqKvKfgeZG+xHiXOpPpGB9bUUWFzjVdX/jAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:42.896868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98d95bce5aa724b08849d7ad648dfde7be1078eff3cfa2aea9bf6f16ec9d77a1","sha256:1008a825d85f4ed93db62200f1fb8f395d852eb54f179f8bec315cef5e377b68"],"state_sha256":"1287017bc9b3eb31bcfb9f0bef2e0790639c9bb4e8b26ff969aac31a4016407a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETVVdZxrGhg4IXYbJgHZRRIGXkC/i3Y7+DcVsxkT8sevQWCjhRxv1QFdN1E+RxFj4ICe4Py22OfceBQoV3oNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:14:52.903401Z","bundle_sha256":"4fb1336a59385bf96d5275923c0b65c8d3255f88d259d788bac77947b9fc32a1"}}